Hi all,
I need eigen values and vectors for symmetric matrices (like VCV).
Solving with numarray and testing the results, I've got
strange results - input and output matrices of some sizes are
very different. That's an example of differencies:
Size MaxDif(E.Val) MaxDif(E.Vect)
2 0 1.110223e-016
3 1.776357e-015 2.053913e-015
10 1.221245e-015 7.255307e-014
11 3.552714e-015 0.8455322
12 1.526557e-016 1.345035e-013
13 8.881784e-016 0.7796273
14 2.775558e-016 0.7504375
15 2.331468e-015 2.045031e-013
This is for numarray 0.7 on W2K.
I hoped to have all the differencies below 1e-15 or so.
What's wrong ? Program text is below.
Thanks,
Eugene Druker
import numarray, numarray.linear_algebra
EigenVectors = numarray.linear_algebra.eigenvectors
Multiply = numarray.matrixmultiply
Zeros = numarray.zeros
Transpose = numarray.transpose
def makeCovMat(size):
covmat = Zeros((size,size),'f8')
d,t = 0.9,0.8
for i in xrange(size):
v = covmat[i,i] = d
for j in xrange(i+1,size):
v *= t
covmat[i,j] = covmat[j,i] = v
return covmat
print 'Size MaxDif(E.Val) MaxDif(E.Vect)'
for size in [2,3]+range(10,24):
covmat = makeCovMat(size)
eval,evec = EigenVectors(covmat)
# Test S = V L V'
mdiag = Zeros((size,size),'f8') # L
for j in xrange(size):
mdiag[j,j] = eval[j]
testmat = Multiply(Transpose(evec),Multiply(mdiag,evec))
ival,ivec = EigenVectors(testmat)
print ' %3d %-14.7g %-14.7g' % \
(size, (eval-ival).max(), (evec-ivec).max())
